Some syzygies of the generators of the ideal of a border basis scheme

Details Some syzygies of the generators of the ideal of a border basis scheme Some syzygies of the generators of the ideal of a border basis scheme

2009-08-04

arxiv.org/abs/0908.0509v2

Mathematics

Algebraic Geometry

Revised in accordance with referee comments: exposition improved, typos & minor errors fixed. To appear in Collectanea Mathema

Scientific paper

A border basis scheme is an affine scheme that can be viewed as an open subscheme of the Hilbert scheme of \mu points of affine n-space. We study syzygies of the generators of a border basis scheme's defining ideal. These generators arise as the entries of the commutators of certain matrices (the "generic multiplication matrices"). We consider two families of syzygies that are closely connected to these matrices: The first arises from the Jacobi identity, and the second from the fact that the trace of a commutator is 0. Several examples of both types of syzygy are presented, including a proof that the border basis schemes in case n = 2 are complete intersections.

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